The almost lattice isometric copies of c 0 in Banach lattices

Jinxi Chen

Commentationes Mathematicae Universitatis Carolinae (2005)

  • Volume: 46, Issue: 3, page 409-412
  • ISSN: 0010-2628

Abstract

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In this paper it is shown that if a Banach lattice E contains a copy of c 0 , then it contains an almost lattice isometric copy of c 0 . The above result is a lattice version of the well-known result of James concerning the almost isometric copies of c 0 in Banach spaces.

How to cite

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Chen, Jinxi. "The almost lattice isometric copies of $c_0$ in Banach lattices." Commentationes Mathematicae Universitatis Carolinae 46.3 (2005): 409-412. <http://eudml.org/doc/249540>.

@article{Chen2005,
abstract = {In this paper it is shown that if a Banach lattice $E$ contains a copy of $c_\{0\}$, then it contains an almost lattice isometric copy of $c_\{0\}$. The above result is a lattice version of the well-known result of James concerning the almost isometric copies of $c_\{0\}$ in Banach spaces.},
author = {Chen, Jinxi},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {Banach lattice; lattice isometry; almost lattice isometry; copy of $c_\{0\}$; lattice isometry; almost lattice isometry; copy of },
language = {eng},
number = {3},
pages = {409-412},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {The almost lattice isometric copies of $c_0$ in Banach lattices},
url = {http://eudml.org/doc/249540},
volume = {46},
year = {2005},
}

TY - JOUR
AU - Chen, Jinxi
TI - The almost lattice isometric copies of $c_0$ in Banach lattices
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2005
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 46
IS - 3
SP - 409
EP - 412
AB - In this paper it is shown that if a Banach lattice $E$ contains a copy of $c_{0}$, then it contains an almost lattice isometric copy of $c_{0}$. The above result is a lattice version of the well-known result of James concerning the almost isometric copies of $c_{0}$ in Banach spaces.
LA - eng
KW - Banach lattice; lattice isometry; almost lattice isometry; copy of $c_{0}$; lattice isometry; almost lattice isometry; copy of
UR - http://eudml.org/doc/249540
ER -

References

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  1. Aliprantis C.D., Burkinshaw O., Positive Operators, Academic Press, New York, 1985. Zbl1098.47001MR0809372
  2. Diestel J., Sequences and Series in Banach Spaces, Springer, New York, 1984. MR0737004
  3. Hudzik H., Mastylo M., Almost isometric copies of l ∞ in some Banach spaces, Proc. Amer. Math. Soc. 119 (1993), 209-215. (1993) MR1146861
  4. Hudzik H., Banach lattices with order isometric copies of l ∞ , Indag. Math. (N.S.) 9 (1998), 521-527. (1998) MR1691991
  5. James R.C., Uniformly non-square Banach spaces, Ann. of Math. (2) 80 (1964), 542-550. (1964) Zbl0132.08902MR0173932
  6. Luxemburg W.A.J., Zaanen A.C., Riesz Spaces I, North-Holland, Amsterdam-London, 1971. 
  7. Meyer-Nieberg P., Banach Lattices, Springer, Berlin-Heidelberg, 1991. Zbl0743.46015MR1128093

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